Topological Interaction between Loop Structures in Polymer Networks and the Nonlinear Rubber Elasticity

Hirayama, Naomi; Tsurusaki, Kyoichi

doi:10.1678/rheology.39.65

Cited by 9 publications

(7 citation statements)

References 26 publications

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“…In the case of melt‐cured networks with many entanglement couplings, the I 2 term has often been attributed to the entanglement effect, but this is not so in the case of Tetra‐PEG gels. In addition to the trapped‐entanglement effect, several concepts such as nematic interaction, excluded volume effect and topological interaction have been proposed so far as the origin of the deviation from classical theories. At present, it is difficult to evaluate unambiguously the concept that accounts for the present results because most of these concepts involve phenomenological model parameters.…”

Section: Tetra‐peg Hydrogelsmentioning

confidence: 99%

New aspects of nonlinear elasticity of polymer gels and elastomers revealed by stretching experiments in various geometries

Urayama

2016

Polymer International

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This review focuses on the novel features of nonlinear elasticity for a range of gels and elastomers that were recently revealed through experiments using various types of strain such as uniaxial and biaxial stretching. Particular emphasis is placed on the magnitude of the cross-effect of strains in different directions which can be characterized by unequal biaxial stretching. The studied materials include (1) markedly swollen hydrogels with a water content of 98%, (2) tetra-arm poly(ethylene glycol) (Tetra-PEG) gels with nearly uniform network structures without entanglement couplings of network strands, (3) slide-ring gels with movable crosslinks along network strands and (4) elastomer foams with low densities of polymer solids. The magnitude of the cross-effect of strains reflects the structural features of networks and crosslinks as well as bulk compressibility for each material. We also summarize recent results on strain-driven swelling and the accompanying force reduction phenomena under various types of stretching. Remaining issues to be investigated are presented on the basis of existing results. SUMMARY AND PERSPECTIVESBiaxial stretching experiments enable us not only to explore the nonlinear stress − strain relations in various types of strain, but to reveal the cross-effect of strains (characterized by the contribution Polym Int 2017; 66: [195][196][197][198][199][200][201][202][203][204][205][206]

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Section: Tetra‐peg Hydrogelsmentioning

confidence: 99%

New aspects of nonlinear elasticity of polymer gels and elastomers revealed by stretching experiments in various geometries

Urayama

2016

Polymer International

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“…The second approach is the topological interactions between loop structures in polymer networks. [61][62][63][64] They assumed the ringshaped structures or loops as structural elements of a crosslinked network, and theoretically considered the elastic effects originating from the constraints that the topologies of the J. Chem. Phys.…”

Section: Conjecture On the Origin Of The Cross Effect Of Strainsmentioning

confidence: 99%

“…Hirayama and Tsurusaki showed that such topological effect results in an explicit cross-effect of strains even for the networks without entanglement loops. 64 The third approach considers the excluded volume effect as the source of interchain and intrachain interactions. 65 These interactions are pronounced in the high concentration region, and transmit the tension among the chains, resulting in a finite cross-effect.…”

Section: Conjecture On the Origin Of The Cross Effect Of Strainsmentioning

confidence: 99%

Probing the cross-effect of strains in non-linear elasticity of nearly regular polymer networks by pure shear deformation

Katashima

Urayama

Chung

et al. 2015

The Journal of Chemical Physics

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The pure shear deformation of the Tetra-polyethylene glycol gels reveals the presence of an explicit cross-effect of strains in the strain energy density function even for the polymer networks with nearly regular structure including no appreciable amount of structural defect such as trapped entanglement. This result is in contrast to the expectation of the classical Gaussian network model (Neo Hookean model), i.e., the vanishing of the cross effect in regular networks with no trapped entanglement. The results show that (1) the cross effect of strains is not dependent on the network-strand length; (2) the cross effect is not affected by the presence of non-network strands; (3) the cross effect is proportional to the network polymer concentration including both elastically effective and ineffective strands; (4) no cross effect is expected exclusively in zero limit of network concentration in real polymer networks. These features indicate that the real polymer networks with regular network structures have an explicit cross-effect of strains, which originates from some interaction between network strands (other than entanglement effect) such as nematic interaction, topological interaction, and excluded volume interaction.

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“…Furthermore, there are many interesting topics related to the topological effects of ring polymers: the probability of forming a local knot in a random polygon [ 111 , 112 ], flat knots (i.e., knotted ring polymers in two dimensions) [ 113 , 114 ], the mean square radius of gyration of ring polymers in melt [ 115 , 116 , 117 , 118 , 119 ], the minimal step number of a lattice knot [ 120 , 121 ], the relaxation dynamics of a knotted ring polymer in solution [ 122 ], etc. [ 123 , 124 ].…”

Section: Introductionmentioning

confidence: 99%

Statistical and Dynamical Properties of Topological Polymers with Graphs and Ring Polymers with Knots

Deguchi

Uehara

2017

Polymers

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We review recent theoretical studies on the statistical and dynamical properties of polymers with nontrivial structures in chemical connectivity and those of polymers with a nontrivial topology, such as knotted ring polymers in solution. We call polymers with nontrivial structures in chemical connectivity expressed by graphs “topological polymers”. Graphs with no loop have only trivial topology, while graphs with loops such as multiple-rings may have nontrivial topology of spatial graphs as embeddings in three dimensions, e.g., knots or links in some loops. We thus call also such polymers with nontrivial topology “topological polymers”, for simplicity. For various polymers with different structures in chemical connectivity, we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We evaluate the ratio of the gyration radius to the hydrodynamic radius, which we expect to be universal from the viewpoint of the renormalization group. Furthermore, we show that the short-distance intrachain correlation is much enhanced for real topological polymers (the Kremer–Grest model) expressed with complex graphs. We then address topological properties of ring polymers in solution. We define the knotting probability of a knot K by the probability that a given random polygon or self-avoiding polygon of N vertices has the knot K. We show a formula for expressing it as a function of the number of segments N, which gives good fitted curves to the data of the knotting probability versus N. We show numerically that the average size of self-avoiding polygons with a fixed knot can be much larger than that of no topological constraint if the excluded volume is small. We call it “topological swelling”.

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Topological Interaction between Loop Structures in Polymer Networks and the Nonlinear Rubber Elasticity

Cited by 9 publications

References 26 publications

New aspects of nonlinear elasticity of polymer gels and elastomers revealed by stretching experiments in various geometries

New aspects of nonlinear elasticity of polymer gels and elastomers revealed by stretching experiments in various geometries

Probing the cross-effect of strains in non-linear elasticity of nearly regular polymer networks by pure shear deformation

Statistical and Dynamical Properties of Topological Polymers with Graphs and Ring Polymers with Knots

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